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finite period, we can make one of three assumptions.

The most conservative one is that the project ceases to exist and that its assets are

â€¢

worthless. In that case, the final year of operation will reflect only the operating

cashflows from that year.

We can assume that the project will end at the end of the analysis period and that the

â€¢

assets will be sold for salvage. While we can try to estimate salvage value directly, a

common assumption that is made is that salvage value is equal to the book value of

the assets. For fixed assets, this will be the undepreciated portion of the initial

investment whereas for working capital, it will be the aggregate value of the

investments made in working capital over the course of the project life.

We can also assume that the project will not end at the end of the analysis period and

â€¢

try to estimate the value of the project on an ongoing basis â€“ this is the terminal value.

In the Disney theme park analysis, for instance, we assumed that the cashflows will

continue forever and grow at the inflation rate each year. If that seems too optimistic,

we can assume that the cashflows will continue wth no growth or even that they will

drop by a constant rate each year.

The right approach to use will depend upon the project being analyzed. For projects that

are not expected to last for long periods, we can use either of the first two approaches; a

zero salvage value should be used if the project assets are likely to become obsolete by

the end of the project life (example: computer hardware) and salvage can be set to book

value if the assets are likely to retain significant value (example: buildings).

For projects with long lives, the terminal value approach is likely to yield more

reasonable results but with one caveat. The investment and maintenance assumptions

made in the analysis should reflect its long life. In particular, capital maintenance

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expenditures will be much higher for projects with terminal value since the assets have to

retain their earning power. In the Disney theme park, the capital maintenance

expenditures climb over time and become larger than depreciation as we approach the

terminal year.

5.10. â˜ž: Currency Choices and NPV

A company in a high inflation economy has asked for your advice regarding which

currency to use for investment analysis. The company believes that using the local

currency to estimate the NPV will yield too low a value, because domestic interest rates

are very high - this, in turn, would push up the discount rate. Is this true?

a. Yes. A higher discount rate will lead to lower NPV

b. No.

Explain your answer.

NPV: Firm versus Equity Analysis

In the analysis above, the cashflows that we discounted were prior to interest and

principal payments and the discount rate we used was the weighted average cost of

capital. In NPV parlance, we were discounting cashflows to the entire firm (rather than

just its equity investors) at a discount rate that reflected the costs to different claimholders

in the firm to arrive at a net present value. There is an alternative. We could have

discounted the cashflows left over after debt payments for equity investors at the cost of

equity and arrived at a net present value to equity investors.

Will the two approaches yield the same net present value? As a general rule, they

will but only if the following assumptions hold:

The debt is correctly priced and the market interest rate to compute the cost of capital

â€¢

is the right one, given the default risk of the firm. If not, it is possible that equity

investors can gain (if interest rates are set too low) or lose (if interest rates are set too

high) to bondholders. This, in turn, can result in the net present value to equity being

different from the net present value to the firm.

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The same assumptions are made about the financing mix used in both calculations.

â€¢

Note that the financing mix assumption affects the discount rate (cost of capital) in

the firm approach and the cashflows (through the interest and principal payments) in

the equity approach.

Given that the two approaches yield the same net present value, which one should we

choose to use? Many practitioners prefer discounting cashflows to the firm at the cost of

capital, because it is easier to do, since the cashflows are before debt payments and we do

not therefore have to estimate interest and principal payments explicitly. Cashflows to

equity are more intuitive, though, since most of us think of cashflows left over after

interest and principal payments as residual cashflows.

Illustration 5.14: NPV from the Equity Investorsâ€™ Standpoint- Paper Plant for Aracruz

The net present value is computed from the equity investorsâ€™ standpoint for the

proposed linerboard plant, for Aracruz, using real cash flows to equity, estimated in

exhibit 5.4 and a real cost of equity of 11.40 %. Table 5.16 summarizes the cashflows and

the present values.

Table 5.16: FCFE on Linerboard Plant (in â€˜000s)

Year FCFE PV of FCFE

0 (185,100 BR) (185,100 BR)

1 34,375 BR 30,840 BR

2 37,201 BR 29,943 BR

3 40,945 BR 29,568 BR

4 45,971 BR 29,784 BR

5 (5,411 BR) (3,145 BR)

6 46,842 BR 24,427 BR

7 46,661 BR 21,830 BR

8 46,470 BR 19,505 BR

9 46,270 BR 17,424 BR

10 163,809 BR 55,342 BR

NPV 70,418 BR

The net present value of 70.418 million BR suggests that this is a good project for

Aracruz to take on.

The analysis was done entirely in real terms, but using nominal cashflows and

discount rate would have had no impact on the net present value. The cashflows will be

higher because of expected inflation but the discount rate will increase by exactly the

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same magnitude, thus resulting in an identical net present value. The choice between

nominal and real cash flows therefore boils down to one of convenience. When inflation

rates are low, it is better to do the analysis in nominal terms since taxes are based upon

nominal income. When inflation rates are high and volatile, it is easier to do the analysis

in real terms or in a different currency with a lower expected inflation rate.

5.11. â˜ž: Equity, Debt and Net Present Value

In the project described above, assume that Aracruz had used all equity to finance the

project, instead of its mix of debt and equity. Which of the following is likely to occur to

the NPV?

a. The NPV will go up, because the cash flows to equity will be much higher; there will

be no interest and principal payments to make each year.

b. The NPV will go down, because the initial investment in the project will much higher

c. The NPV will remain unchanged, because the financing mix should not affect the

NPV

d. The NPV might go up or down, depending upon .....

Explain your answer.

Properties of the NPV Rule

The net present value has several important properties that make it an attractive

decision rule.

1. Net present values are additive

Assets in Place: These are the assets already owned by a

The net present values of firm, or projects that it has already taken.

individual projects can be aggregated

to arrive at a cumulative net present value for a business or a division. No other

investment decision rule has this property. The property itself raises a number of

implications.

The value of a firm can be written in terms of the net present values of the projects it

â€¢

has already taken on as well as the net present values of prospective future projects

Value of a Firm = ! Present Value of Projects in Place + ! NPV of expected future projects

The first term in this equation captures the value of assets in place, while the second

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term measures the value of expected future growth. Note that the present value of

projects in place is based on anticipated future cash flows on these projects.

When a firm terminates an existing project that has a negative present value based on

â€¢

anticipated future cash flows, the value of the firm will increase by that amount.

Similarly, when a firm takes on a new project, with a negative net present value, the

value of the firm will decrease by that amount.

When a firm divests itself of an existing asset, the price received for that asset will

â€¢

affect the value of the firm. If the price received exceeds the present value of the

anticipated cash flows on that project to the firm, the value of the firm will increase

with the divestiture; otherwise, it will decrease.

When a firm invests in a new project with a positive net present value, the value of

â€¢

the firm will be affected depending upon whether the NPV meets expectations. For

example, a firm like Microsoft is expected to take on high positive NPV projects and

this expectation is built into value. Even if the new projects taken on by Microsoft

have positive NPV, there may be a drop in value if the NPV does not meet the high

expectations of financial markets.

When a firm makes an acquisition, and pays a price that exceeds the present value of

â€¢

the expected cash flows from the firm being acquired, it is the equivalent of taking on

a negative net present value project and will lead to a drop in value.

2. Intermediate Cash Flows are invested at the hurdle rate

Implicit in all present value calculations are assumptions about the rate at which

intermediate cash flows get reinvested. The net

Hurdle Rate: This is the minimum

present value rule assumes that intermediate cash

acceptable rate of return that a firm will

flows on a projects â€“â€“, i.e., cash flows that occur accept for taking a given project.

between the initiation and the end of the project

â€“â€“ get reinvested at the hurdle rate, which is the cost of capital if the cash flows are to the

firm and the cost of equity if the cash flows are to equity investors. Given that both the

cost of equity and capital are based upon the returns that can be made on alternative

investments of equivalent risk, this assumption should be a reasonable one.

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3. NPV Calculations allow for expected term structure and interest rate shifts

In all the examples throughout in this chapter, we have assumed that the discount

rate remains unchanged over time. This is not always the case, however; the net present

value can be computed using time-varying discount rates. The general formulation for the

NPV rule is as follows

t=N

CFt

"

NPV of Project = - Initial Investment

j=t

t=1

! (1 + rt )

j =1

where

CFt = Cash flow in period t

rt = One-period Discount rate that applies to period t

N = Life of the project

The discount rates may change for three reasons:

The level of interest rates may change over time and the term structure may provide

â€¢

some insight on expected rates in the future.

The risk characteristics of the project may be expected to change in a predictable way

â€¢

over time, resulting in changes in the discount rate.

The financing mix on the project may change over time, resulting in changes in both

â€¢

the cost of equity and the cost of capital.

Illustration 5.15: NPV Calculation With Time-Varying Discount Rates

Assume that you are analyzing a 4-year project, investing in computer software

development. Further, assume that the technological uncertainty associated with the

software industry leads to higher discount rates in future years.

The present value of each of the cash flows can be computed as follows â€“

PV of Cash Flow in year 1 = $ 300 / 1.10 = $ 272.72

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PV of Cash Flow in year 2 = $ 400/ (1.10 * 1.11) = $ 327.60

PV of Cash Flow in year 3 = $ 500/ (1.10 * 1.11 * 1.12) = $ 365.63

PV of Cash Flow in year 4 = $ 600/ (1.10 * 1.11 * 1.12 * 1.13) = $ 388.27

NPV of Project = $ 272.72+ $ 327.60+ $ 365.63+ $ 388.27 - $ 1000.00 = $354.23

5.12. â˜ž: Changing Discount Rates and NPV

In the above analysis, assume that you had been asked to use one discount rate for all of

the cash flows. Is there a discount rate that would yield the same NPV as the one above?

a. Yes

b. No

If yes, how would you interpret this discount rate?

Biases, Limitations, and Caveats

In spite of its advantages and its linkage to the objective of value maximization,

the net present value rule continues to have its detractors, who point out several

limitations

The net present value is stated in absolute rather than relative terms and does not,

â€¢

therefore, factor in the scale of the projects. Thus, project A may have a net present

value of $200, while project B has a net present value of $100, but project A may

require an initial investment that is ten or 100 times larger than project B. Proponents

of the NPV rule argue that it is surplus value, over and above the hurdle rate, no

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